Dear MO-community, I am not sure how mature my view on this is and I might say some things that are controversial. I welcome contradicting views. In any case, I find it important to clarify this in my ...

I sort of understand the definition of a spectral sequence and am aware that it is an indispensable tool in modern algebraic geometry and topology. But why is this the case, and what can one do with ...

Tropical geometry can be described as "algebraic geometry" over the semifield $\mathbb{T}$ of tropical numbers. As a set, $\mathbb{T}=\mathbb{R}\cup \{ -\infty\}$; this is endowed with addition being ...

A basic construction in algebraic topology is the localization of spaces or spectra with respect to a homology theory: one formally inverts the $E$-homology isomorphisms, reflecting each space into ...

Dear All!
There is a trend, for some people, to study representations of quivers. The setting of the problem is undoubtedly natural, but representations of quivers are present in the literature for ...

I am teaching an advanced undergraduate class on topology. We are doing introductory knot theory at the moment. One of my students asked how do we know to use this skein relation to compute all these ...

I am starting to dive into a study of Several Complex Variables. I would like to have a few guiding examples of "big payoffs". These should be very natural sounding theorems which depend on a lot of ...

As I understand it, rooted maps on surfaces were first introduced in enumerative combinatorics because they are easier to count than unrooted maps, which can have non-trivial symmetries. A map is a ...